Question

solve for u.
20u² - 55 = -10
write your answers as integers or as proper or improper fractions in simplest for
u = or u =

Explanation:

Step1: Isolate the quadratic term

Add 55 to both sides of the equation \(20u^{2}-55 = - 10\).
\(20u^{2}-55 + 55=-10 + 55\)
\(20u^{2}=45\)

Step2: Solve for \(u^{2}\)

Divide both sides by 20.
\(u^{2}=\frac{45}{20}\)
Simplify the fraction \(\frac{45}{20}\) by dividing numerator and denominator by 5, we get \(u^{2}=\frac{9}{4}\)

Step3: Solve for \(u\)

Take the square root of both sides. Remember that when we take the square root of a number, we get both positive and negative roots.
\(u=\pm\sqrt{\frac{9}{4}}\)
Since \(\sqrt{\frac{9}{4}}=\frac{3}{2}\), then \(u = \frac{3}{2}\) or \(u=-\frac{3}{2}\)

Answer:

\(u=\frac{3}{2}\) or \(u = -\frac{3}{2}\)